The crossed product of a $C^{\ast }$-algebra by an endomorphism
HTML articles powered by AMS MathViewer
- by William L. Paschke PDF
- Proc. Amer. Math. Soc. 80 (1980), 113-118 Request permission
Abstract:
Let A be a unital, strongly amenable ${C^ \ast }$-algebra, $\sigma :A \to pAp$ a $^ \ast$-isomorphism (where p is a proper projection of A), and S an isometry such that $Sx{S^ \ast } = \sigma (x)$ for all x in A. If A has no nontrivial $\sigma$-invariant ideals, then ${C^ \ast }(A,S)$ is simple. Furthermore, ${C^\ast }(A,S)$ is isomorphic to a corner of the crossed product of $A \otimes$ (compacts) by an automorphism.References
- Lawrence G. Brown, Stable isomorphism of hereditary subalgebras of $C^*$-algebras, Pacific J. Math. 71 (1977), no. 2, 335–348. MR 454645, DOI 10.2140/pjm.1977.71.335
- John Bunce, Respresentations of strongly amenable $C^{\ast }$-algebras, Proc. Amer. Math. Soc. 32 (1972), 241–246. MR 295091, DOI 10.1090/S0002-9939-1972-0295091-8
- John W. Bunce and William L. Paschke, Quasi-expectations and amenable von Neumann algebras, Proc. Amer. Math. Soc. 71 (1978), no. 2, 232–236. MR 482252, DOI 10.1090/S0002-9939-1978-0482252-3
- A. Connes, On the cohomology of operator algebras, J. Functional Analysis 28 (1978), no. 2, 248–253. MR 0493383, DOI 10.1016/0022-1236(78)90088-5
- Joachim Cuntz, Simple $C^*$-algebras generated by isometries, Comm. Math. Phys. 57 (1977), no. 2, 173–185. MR 467330, DOI 10.1007/BF01625776 J. Cuntz and G. K. Pedersen, Equivalence and KMS states on ${C^\ast }$-dynamical systems, preprint, 1978. M. M. Day, Normed linear spaces, Springer-Verlag, Berlin, 1962.
- Dorte Olesen and Gert Kjaergȧrd Pedersen, Some $C^{\ast }$-dynamical systems with a single KMS state, Math. Scand. 42 (1978), no. 1, 111–118. MR 500150, DOI 10.7146/math.scand.a-11740
- Jonathan Rosenberg, Amenability of crossed products of $C^*$-algebras, Comm. Math. Phys. 57 (1977), no. 2, 187–191. MR 467331, DOI 10.1007/BF01625777
- Jonathan Rosenberg, Appendix to: “Crossed products of UHF algebras by product type actions” [Duke Math. J. 46 (1979), no. 1, 1–23; MR 82a:46063 above] by O. Bratteli, Duke Math. J. 46 (1979), no. 1, 25–26. MR 523599
- Hiroshi Takai, On a duality for crossed products of $C^{\ast }$-algebras, J. Functional Analysis 19 (1975), 25–39. MR 0365160, DOI 10.1016/0022-1236(75)90004-x
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 113-118
- MSC: Primary 46L05; Secondary 46L55
- DOI: https://doi.org/10.1090/S0002-9939-1980-0574518-2
- MathSciNet review: 574518